1. Field of the Invention
The present invention relates to a three-dimensional machining method for machining a workpiece three-dimensionally with a machine tool such as a milling cutter, and more particularly to a processing control for defining a surface to be machined and generating paths of a cutting tool to machine the surface.
2. Description of Related Art
Recently, computerized three-dimensional machining of a metal workpiece has been developed for practical use. The three-dimensional machining is generally performed based on either paths of the working end of a ball tip of a cutting tool or paths of the center of the ball tip of the cutting tool.
In either method, conventionally, a plurality of surfaces to be machined are defined individually, and continuous surfaces are machined by transfer cutting. For example, as shown in FIGS. 7a and 7b, three continuous surfaces #i, #j and #k are defined individually (in individual coordinate systems (u, v)) and are machined continuously by transferring a cutting tool from a path to machine the surface #i to a path to machine the surface #k and then to a path to machine the surface #j. In the transfer cutting, generation of tool paths is sometimes performed based on a direction .gamma. which does not reflect the characteristics of all the surfaces. In this case, the transfer cutting is not in accordance with the characteristics of the surfaces, and the cutting may be rough or may be unnecessarily minute and wasteful. Further, for transfer cutting, a large volume of processing to avoid interference of the cutting tool is necessary, which takes a lot of time.
In order to solve the above problems, the applicant suggested, in U.S. Pat. No. 5,515,290, a three-dimensional machining method wherein a plurality of curved surfaces which have distinct characteristics are defined as a unified surface by a group of polynomials with the fourth or less degree with respect to parameters u and v, and paths of a cutting tool to machine the unified surface are calculated by using the polynomials. According to this method, the solutions can be obtained arithmetically, and points on the unified curved surface expressed in the coordinate system (u, v) can be converted into values in the rectangular coordinate system (x, y, z) speedily and vice versa. However, curved surfaces are generally defined in forms of spline, B-spline, nurbus, etc. and are not always defined by polynomials, and therefore, in order to carry out calculation control in the above method using expressions in other forms, some conversion is necessary.